Introduction to the Modeling and Analysis of Complex Systems

ivReviewer’s NotesThis book provides an excellent introduction to the field of modeling and analysis of complexsystems to both undergraduate and graduate students in the physical sciences, socialsciences, health sciences, humanities, and engineering. Knowledge of basic mathematicsis presumed of the reader who is given glimpses into the vast, diverse and rich world ofnonlinear algebraic and differential equations that model various real-world phenomena.The treatment of the field is thorough and comprehensive, and the book is written in avery lucid and student-oriented fashion. A distinguishing feature of the book, which usesthe freely available software Python, is numerous examples and hands-on exercises oncomplex system modeling, with the student being encouraged to develop and test his orher own code in order to gain vital experience.The book is divided into three parts. Part I provides a basic introduction to the artand science of model building and gives a brief historical overview of complex systemmodeling. Part II is concerned with systems having a small number of variables. Afterintroducing the reader to the important concept of phase space of a dynamical system,it covers the modeling and analysis of both discrete- and continuous-time systems in asystematic fashion. A very interesting feature of this part is the analysis of the behavior ofsuch a system around its equilibrium state, small perturbations around which can lead tobifurcations and chaos. Part III covers the simulation of systems with a large number ofvariables. After introducing the reader to the interactive simulation tool PyCX, it presentsthe modeling and analysis of complex systems (e.g., waves in excitable media, spreadof epidemics and forest fires) with cellular automata. It next discusses the modeling andanalysis of continuous fields that are represented by partial differential equations. Examplesare diffusion-reaction systems which can exhibit spontaneous self-organizing behavior(e.g., Turing pattern formation, Belousov-Zhabotinsky reaction and Gray-Scott patternformation). Part III concludes with the modeling and analysis of dynamical networks andagent-based models.The concepts of emergence and self-organization constitute the underlying thread thatweaves the various chapters of the book together.About the Reviewer: Dr. Siddharth G. Chatterjee received his Bachelor’s Degree in Technology(Honors) from the Indian Institute of Technology, Kharagpur, India, and M.S. andPh.D. degrees from Rensselaer Polytechnic Institute, Troy, New York, USA, all in ChemicalEngineering. He has taught a variety of engineering and mathematical courses andhis research interests are the areas of philosophy of science, mathematical modeling andsimulation. Presently he is Associate Professor in the Department of Paper and BioprocessEngineering at SUNY College of Environmental Science and Forestry, Syracuse,